Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. How many times do the hands of a clock overlap in a 12-hour period?

A. 10 times
B. 11 times
C. 12 times
D. 9 times

Solution

The hands of a clock overlap 11 times in a 12-hour period.

Correct Answer: B — 11 times

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Q. How many ways can 10 different trophies be awarded to 3 different winners?

A. 1000
B. 720
C. 1200
D. 100

Solution

The number of ways to award trophies is P(10, 3) = 10! / (10-3)! = 720.

Correct Answer: A — 1000

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Q. How many ways can 2 boys and 3 girls be selected from a group of 5 boys and 6 girls?

A. 100
B. 60
C. 80
D. 120

Solution

The number of ways is C(5, 2) * C(6, 3) = 10 * 20 = 200.

Correct Answer: A — 100

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Q. How many ways can 3 different prizes be awarded to 5 students?

A. 60
B. 100
C. 120
D. 30

Solution

The number of ways to award 3 prizes to 5 students is P(5, 3) = 60.

Correct Answer: C — 120

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Q. How many ways can 4 different books be arranged on a shelf if 2 specific books must be together?

A. 48
B. 24
C. 36
D. 60

Solution

Treat the 2 specific books as one unit. So, we have 3 units to arrange: (2 books together + 2 other books) = 3! * 2! = 12.

Correct Answer: A — 48

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Q. How many ways can 4 different colored balls be arranged in a row?

A. 24
B. 16
C. 12
D. 8

Solution

The number of ways to arrange 4 different colored balls is 4! = 24.

Correct Answer: A — 24

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Q. How many ways can 4 people be seated at a round table?

A. 6
B. 12
C. 24
D. 30

Solution

The number of arrangements of 4 people at a round table is (4-1)! = 3! = 6.

Correct Answer: A — 6

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Q. How many ways can 4 people be selected from a group of 12?

A. 495
B. 300
C. 400
D. 600

Solution

The number of ways to select 4 people from 12 is C(12, 4) = 495.

Correct Answer: A — 495

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Q. How many ways can 5 books be arranged on a shelf?

A. 60
B. 120
C. 100
D. 24

Solution

The number of arrangements of 5 distinct books is 5! = 120.

Correct Answer: B — 120

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Q. How many ways can 5 different books be chosen from a shelf of 15 books?

A. 3003
B. 5005
C. 1001
D. 1365

Solution

The number of ways to choose 5 books from 15 is C(15, 5) = 3003.

Correct Answer: A — 3003

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Q. How many ways can 5 different books be selected and arranged on a shelf?

A. 120
B. 60
C. 30
D. 24

Solution

The number of ways to select and arrange 5 books is 5! = 120.

Correct Answer: A — 120

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Q. How many ways can 5 different colored balls be placed in 3 different boxes?

A. 243
B. 125
C. 3125
D. 729

Solution

Each ball can go into any of the 3 boxes, so the total ways = 3^5 = 243.

Correct Answer: A — 243

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Q. How many ways can 5 different letters be arranged if 2 letters must be together?

A. 48
B. 60
C. 72
D. 80

Solution

Treat the 2 letters as one unit, so we have 4 units to arrange: 4! * 2! = 48.

Correct Answer: C — 72

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Q. How many ways can 5 different prizes be awarded to 3 students if each student can receive more than one prize?

A. 243
B. 125
C. 81
D. 64

Solution

Each prize can go to any of the 3 students, so there are 3^5 = 243 ways.

Correct Answer: A — 243

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Q. How many ways can 5 different prizes be distributed among 3 students?

A. 243
B. 125
C. 60
D. 30

Solution

Each prize can go to any of the 3 students. Therefore, the total ways = 3^5 = 243.

Correct Answer: A — 243

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Q. How many ways can 6 different colored balls be arranged in a row?

A. 720
B. 600
C. 840
D. 480

Solution

The number of arrangements of 6 different colored balls is 6! = 720.

Correct Answer: A — 720

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Q. How many ways can 6 people be seated in a round table?

A. 720
B. 120
C. 60
D. 30

Solution

The number of ways to arrange 6 people in a round table is (6-1)! = 5! = 120.

Correct Answer: A — 720

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Q. How many ways can 6 people be seated in a row if two specific people must sit next to each other?

A. 120
B. 720
C. 240
D. 60

Solution

Treat the two specific people as one unit. Then, we have 5 units to arrange: 5! = 120. The two people can be arranged in 2! ways. Total = 120 * 2 = 240.

Correct Answer: A — 120

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Q. How many ways can 7 different books be arranged on a shelf if 2 specific books must be together?

A. 720
B. 1440
C. 5040
D. 840

Solution

Treat the 2 specific books as one unit. Then, arrange 6 units: 6! * 2! = 1440.

Correct Answer: B — 1440

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Q. How many ways can a committee of 3 be formed from 8 people?

A. 56
B. 48
C. 40
D. 36

Solution

The number of ways to form a committee is C(8,3) = 56.

Correct Answer: A — 56

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Q. How many ways can the letters of the word 'BANANA' be arranged?

A. 60
B. 30
C. 20
D. 10

Solution

The number of arrangements is 6! / (3!) = 20.

Correct Answer: B — 30

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Q. How many ways can you choose 2 fruits from 5 different fruits?

A. 10
B. 5
C. 15
D. 20

Solution

The number of ways to choose 2 fruits from 5 is C(5, 2) = 5! / (2! * (5-2)!) = 10.

Correct Answer: A — 10

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Q. How many ways can you select 3 out of 7 different colored shirts?

A. 35
B. 21
C. 7
D. 14

Solution

The number of ways to select 3 shirts from 7 is C(7, 3) = 35.

Correct Answer: A — 35

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Q. How many ways can you select 4 cards from a deck of 52 cards?

A. 270725
B. 130816
C. 22100
D. 10000

Solution

The number of ways to select 4 cards from 52 is C(52, 4) = 270725.

Correct Answer: A — 270725

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Q. How much will $3000 amount to after 4 years at a compound interest rate of 7% per annum?

A. $4000.00
B. $4005.00
C. $4002.00
D. $4003.00

Solution

Amount = P(1 + r/n)^(nt) = 3000(1 + 0.07/1)^(1*4) = 3000(1.3107961) = 3932.39

Correct Answer: A — $4000.00

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Q. Identify the odd number in the series: 3, 6, 9, 12, 15, 18, 21, 24, 27.

A. 9
B. 12
C. 15
D. 27

Solution

All numbers are multiples of 3 except 27, which is not part of the even multiples.

Correct Answer: D — 27

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Q. Identify the odd one out in the series: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

A. 1
B. 3
C. 5
D. 19

Solution

All numbers are odd except 1, which is not considered an odd number in this context.

Correct Answer: A — 1

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Q. Identify the odd one out in the series: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

A. 16
B. 25
C. 36
D. 49

Solution

All numbers are perfect squares except 49, which is not a perfect square in this context.

Correct Answer: D — 49

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Q. Identify the odd one out: 10%, 30%, 50%, 70%, 90%.

A. 10%
B. 30%
C. 50%
D. 70%

Solution

10% is the odd one out as it is the only percentage that is less than 30%.

Correct Answer: A — 10%

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Q. Identify the odd one out: 12%, 15%, 18%, 20%, 24%.

A. 12%
B. 15%
C. 18%
D. 20%

Solution

20% is the odd one out as it does not fit the pattern of increasing by 3%.

Correct Answer: D — 20%

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Arithmetic Aptitude

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